A theorem about states on quantum logics. States on Jordan algebras
Let \({\mathcal A}\) be a Jordan algebra of operators on a complex Hilbert space and let \(\mu\) be a state on the projections of \({\mathcal A}\) (i.e. \(\mu\) is positive and orthoadditive). The author proves that every state \(\mu\) has an extension to a normal linear functional on \({\mathcal A}\), in case \({\mathcal A}\) is a continuous hyperfinite Jordan factor. He also notes that using a result of \textit{E. Christensen} [Commun. Math. Phys. 86, 529- 538 (1982; Zbl 0507.46052)], this can be extended to the case where \({\mathcal A}\) is an arbitrary continuous infinite Jordan algebra.
scientific article; zbMATH DE number 3863886